Changing Equations | quadratics101

Completing the Square

You complete the sqaure in order to convert quadratics from standard from to vertex from. By having your equation in vertex form, you can easily find the vertx. Connection: Recall that you look at the h-value in order to find the x-value of the vertex and you look at the k-value in order to find the y-value of the vertex. Note: the h-value is a negative (so, the x-value would have the opposite symbol than the h-value in the equation)

Steps to take:

1. Remove the common factor from the x and the x-term.

2. Find the constant that must be added and subtracted to create a perfect square. Rewrite the expression by adding and subtracting that constant. To find the constant you would divide the x-term by 2, then square it.

3. Group the three terms that form the perfect sqaure. First, move the subtracted constant outside of the bracket by multipling it by the common factor in step. Collect the "like terms".

4. Factor the perfect sqaure.

Connection: In order to factor the perfect sqaure, recall that you must square-root the first and last term and then put thoese in a bracket squared.

Standard Form to Vertex Form

Vertex Form to Standard Form

Standard Form to Factored Form

After factoring your equation using the method of simple trinomials, you can find your zeros. First, set the (x)s to zero. Then, solve for x by isolating it. You can also find the x-value of the vertex by adding the (x) and dividing it by 2. Then, you can find the y-value of the vertex by plugging in the x-value in your equation and solving. All these steps allow you to graph your equation.

After expanding and simplifying, you can find the x-value of the vertex. You can do this by plugging in the values in the equation -b divided by 2 multiplied by 2. Then, you can find the y-value of the vertex by plugging in the x-value into the original equation and solving. In order to find the zeros, you must factor your equation (so you are know in factored form). Then, set the (x)s to zero and solve for x by isolating it. All this allows you to graph your equation.

After completing the square, you can easily find your vertex. The vertex is your h (x-value) and k (y-value) point from the equation. Then, you find your zeros by setting y to zero and isolating x.